Once we know how to strongly antimagic label a given graph \(G\) , big-onellows us to bootstrap this knowledge into the ability to create strongly antimagic labelings for many other graphs, namely those graphs that may be obtained from \(G\)  by adding edges in a way that respects the vertex ordering induced by the strongly antimagic labeling on \(G\) . For example, the results of this paper established that spiders and double spiders are strongly antimagic, which easily yielded that cycle spiders and cycle double spiders are strongly antimagic. As a further example, the results of [1]} established that regular graphs are antimagic and thus strongly antimagic, so regular graphs may also be extended to obtain many more strongly antimagic graphs. It is therefore an enticing challenge to establish that certain families of graphs are strongly antimagic as such results may in fact verify the strongly antimagic property for many graphs beyond those contained in the family.
